Journal
COMPUTER PHYSICS COMMUNICATIONS
Volume 185, Issue 4, Pages 1207-1216Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cpc.2013.12.017
Keywords
High-dimensional problems; DMRG; MPS; Tensor train format; Low-lying eigenstates
Funding
- RFBR [11-01-00549-a, 12-01-33013, 12-01-00546-a, 12-01-91333-nnio-a]
- Rus. Fed. Gov. project [16.740.12.0727]
- President of Russia stipend (S. Dolgov) at the Institute of Numerical Mathematics RAS
- EPSRC at University of Southampton [EP/H003789/2]
- Engineering and Physical Sciences Research Council [EP/F065205/2, EP/F065205/1, EP/H003789/2, EP/H003789/1] Funding Source: researchfish
- EPSRC [EP/H003789/2, EP/F065205/1, EP/H003789/1, EP/F065205/2] Funding Source: UKRI
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We consider approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high-dimensional problems. We use the tensor train (TT) format for vectors and matrices to overcome the curse of dimensionality and make storage and computational cost feasible. We approximate several low-lying eigenvectors simultaneously in the block version of the TT format. The computation is done by the alternating minimization of the block Rayleigh quotient sequentially for all IF cores. The proposed method combines the advances of the density matrix renormalization group (DMRG) and the variational numerical renormalization group (vNRG) methods. We compare the performance of the proposed method with several versions of the DMRG codes, and show that it may be preferable for systems with large dimension and/or mode size, or when a large number of eigenstates is sought. (C) 2013 Elsevier B.V. All rights reserved.
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